Analog linear stroke piezoelectric actuators are well known in the art. They provide a linear stroke, at a force determined by the "stiffness coefficient" of the actuator over a selected range of extension, in response to a voltage excitation signal applied to the piezoelectric material. The piezoelectric material, referred to as the actuator's "displacement generator", is typically a stack of piezoelectric wafers; the polarization axis of each wafer is aligned along the longitudinal axis of the stack to define the actuator's axis of extension. In the absence of a load, the stack is maintained in compression within the actuator housing by a "pre-load" force with a value selected to linearize the stiffness coefficient (Ks) of the displacement generator stack. This allows the actuator extension (D) to be defined in terms of the displacement force (F) by Hooke's law: F=K.sub.S .multidot.D. In operation, the piezoelectric elements are energized by a voltage excitation signal applied simultaneously to the entire stack, inducing an electric field intensity in each wafer. The wafers respond together by extending or contracting in dependence on the polarity of the induced electric field, by an amount proportional to the electric field intensity. By modulating the voltage signal magnitude to vary the electric field intensity, the amount of extension or contraction (retraction) may be controlled.
The piezoelectric actuators provide only small extension range values; less than 0.1% of their length. Their principal utility lies in the precision control of the extension. The incremental value of extension or contraction may be accurately correlated to a corresponding incremental change in the voltage excitation signal. Their drawback, however, is the inability to precisely define an absolute displacement value in terms of an absolute excitation signal magnitude due to the inherent hysteresis characteristic of the piezoelectric material. The hysteresis affects the repeatability of the actuator's mechanical displacement, so as to produce a steady state position (extension) error with respect to the applied excitation voltage signal magnitude. In AC applications this produces a phase lag at the fundamental drive frequency of the excitation signal.
While the actuator control circuitry may account for the position error to some extent, it is limited. The hysteresis decreases with decreasing extention increments, i.e. decreasing excitation signal magnitude, but in a nonlinear manner. This nonlinearity further affects the actuator responsivity; the extension increment value per voltage increment value. The presence of the hysteresis characteristic, compounded by its nonlinear change with decreasing excitation signal magnitude produces inaccuracies in the extension set point values which cannot be fully compensated.